Ok then, what’s the question? I thought it was “What are the chances that the other child is CHOSEN_SEX?”.

By concluding that all combinations of of boy and girl are equally likely you are making a statistical fallacy in assuming that a randomly selected subset has the same properties as the superset.

To illustrate, pretend we have a planet where people can choose to have either one child or two children (for whatever reason, the point is to reduce the sample space). And lets say that 2/3 the population chooses to have one child. Now, by some random chance, all of the people who chose to have one child all had boys. Statistically, that just ruins everything. Because in this scenario, if you have two children, it is more likely that you have two girls.

Why? Because half of all births are already boys. Assuming an even distribution of boys and girl births, we can expect two child couples to have only girls.

To use the general case that it is 50% likely for a given sex during birth as true for all subsets is wrong. Especially since we aren’t scooping up a random subset, but a subset that also exhibits an additional specific quality.

So, in conclusion, we honestly cannot know with any degree of certainty the sex of a given child based on the sex of another child, no matter how you finagle the language. There are simply too many other variables.

It’s also the problem with the “proofs” provided. They all just assume two child families and run data using two child sets without thinking about the likelihood of having a two child set in the first place.

Data from people I know:

My parents: GBGB

My older sister: G

Her husband’s parents: BGB

My wife’s parents: BGG

My younger sister: GGB

My aunt and uncle: GGB

My boss: B

My coworker: B

My step-father: GB

His daughter: GG

My sister’s neighbor: BB

13 girls, 12 boys, 3 two child families out of 11. Not a terribly large sample size, true, but it is representative of the inherent instability of what the question is asking. The people who are claiming 66% are claiming to know more information than than actually have available. The event is so definitely random that the best thing to do is to flip a coin and call it 50%. Anything else is being dishonest on some level.